1 The pion cloud of the nucleon: Facts and popular fantasies Ulf-G. Meißner, Universit¨ at Bonn & FZ J ¨ ulich Supported by DFG, SFB/TR-16 “Subnuclear Structure of Matter” and by EU, I3HP-N5 “Structure and Dynamics of Hadrons” The Pion Cloud of the Nucleon: Facts and popular Fantasies – Ulf-G. Meißner – MIT, LNS, Mar. 9, 2007 ·◦ < ∧ > •
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The pion cloud of the nucleon:Facts and popular fantasies
Ulf-G. Meißner, Universit at Bonn & FZ Julich
Supported by DFG, SFB/TR-16 “Subnuclear Structure of Matter” and by EU, I3HP-N5 “Structure and Dynamics of Hadrons”
The Pion Cloud of the Nucleon: Facts and popular Fantasies – Ulf-G. Meißner – MIT, LNS, Mar. 9, 2007 · ◦ C < ∧ O > B •
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CONTENTS
• Introductory remarks & disclaimer
• Dispersion relations: Theoretical framework
• Discussion of the spectral functions
• Results for space- and time-like ffs& the pion cloud
• Summary and outlook
with: Maxim A. Belushkin, Hans-Werner Hammer
The Pion Cloud of the Nucleon: Facts and popular Fantasies – Ulf-G. Meißner – MIT, LNS, Mar. 9, 2007 · ◦ C < ∧ O > B •
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Introduction
The Pion Cloud of the Nucleon: Facts and popular Fantasies – Ulf-G. Meißner – MIT, LNS, Mar. 9, 2007 · ◦ C < ∧ O > B •
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REMARKS & DISCLAIMER
• Analyze nucleon em ffs using dispersion theory w/ input fromchiral perturbation theory, draw conclusions about the pion cloud
• What can we say (or not) about the pion cloud of the nucleon?
? concept originated soon after Yukawas proposal of the pionHeisenberg, Wentzel, Pauli, Kemmer, . . .
? in general, not a well-defined concept → requires some modelling
? pion cloud = pion loops in CHPT?
yes, but this clearly shows the limitations of the concept
In general, any observable receives contributions frompion loops and short-distance operators → reshufflingsince only physical observables are RG invariant
⇒ let us analyze this in more detail
ddλ O(λ) = 0
The Pion Cloud of the Nucleon: Facts and popular Fantasies – Ulf-G. Meißner – MIT, LNS, Mar. 9, 2007 · ◦ C < ∧ O > B •
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LOOPS vs CONTACT OPERATORS: AN EXAMPLEBernard, Hemmert, M., Nucl. Phys. A 732 (2004) 149 [hep-ph/0307115]
• the isovector Dirac radius of the proton at third order in the chiral expansion
〈r2〉V1 =
(0.61 −
(0.47 GeV−2
)d(λ) + 0.47 log λ
1 GeV
)fm2
− dimension-3 LEC d parameterizes the nucleon “core”
• Leading QCD logs or other αS corrections can be includedsee .e.g. Gari, Krumpelmann, Z. Phys. A 322 (1985) 689 , Mergell, M., Drechsel, Nucl. Phys. A 596 (1996) 367
⇒ severely restricts the number of fit parameters
The Pion Cloud of the Nucleon: Facts and popular Fantasies – Ulf-G. Meißner – MIT, LNS, Mar. 9, 2007 · ◦ C < ∧ O > B •
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SUMMARY: SPECTRAL & FIT FUNCTIONS
• Representation of the pole contributions: vector mesons[NB: can be extended for finite width]
Im FVi (t) =
∑vπav
i δ(t−M2v ) , av
i = M2v
fVgvNN ⇒ Fi(t) =
∑v
avi
M2v −t
• Isovector spectral functions:
Im FVi (t) = Im F
(2π)i (t) +
∑v=ρ′,ρ′′,...
avi δ(t − M 2
v ) , (i = 1 , 2)
• Isoscalar spectral functions:
ImFSi (t) = π ai
ω δ(t−M2ω)+ImF (KK)
i (t)+ImF (πρ)i (t)+
∑v=S′,S′′,...
avi δ(t −M 2
v )
• Parameters: 2 for the ω, 3 (4) for each other V-mesons minus # of constraints
• Ill-posed problem → extra constraint: minimal # of poles to describe the data
The Pion Cloud of the Nucleon: Facts and popular Fantasies – Ulf-G. Meißner – MIT, LNS, Mar. 9, 2007 · ◦ C < ∧ O > B •
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Results
Belushkin, Hammer, M., Phys. Rev. C 75 (2007) 035202 [hep-ph/0608337]
The Pion Cloud of the Nucleon: Facts and popular Fantasies – Ulf-G. Meißner – MIT, LNS, Mar. 9, 2007 · ◦ C < ∧ O > B •
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GENERAL COMMENTS ON THE FITS
• large MC sampling for initial values, successive improvementby pole reduction, new MCs, . . .
M [fm] 0.862 (0.854. . .0.871) 0.879 0.873(11) [6]
[1] Rosenfelder, Phys. Lett. B 479 (2000) 381[2] Sick, private communication[3] Melnikov, van Ritbergen, Phys. Rev. Lett. 84 (2000) 1673[4] Sick, Phys. Lett. B 576 (2003) 62[5] Kopecky et al., Phys. Rev. C 56 (1997) 2229[6] Kubon et al., Phys. Lett. B 524 (2002) 26
? Magnetic radii in good agreement with recent determinations
? Proton electric radius comes out . 0.855 fm
The Pion Cloud of the Nucleon: Facts and popular Fantasies – Ulf-G. Meißner – MIT, LNS, Mar. 9, 2007 · ◦ C < ∧ O > B •
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SPACE-LIKE FORM FACTORS
0 0.5 1 1.50
0.02
0.04
0.06
0.08
0.1
0.12
GEn
0.01 0.1 1 100.5
0.6
0.7
0.8
0.9
1
1.1
GMn /(
µ nGD
)
0.001 0.01 0.1 1Q2 [GeV2]
0.4
0.6
0.8
1
GEp /G
D
0.1 1 10Q2 [GeV2]
0.6
0.7
0.8
0.9
1
1.1
1.2
GMp /(
µ pGD
)
0 0.5
1
0 0.1 0.2
1
0 0.2 0.4
1
• present best fitincl. time-like data
• 4 effective IS poles
• 4 effective IV poles
• weighted χ2/dof = 1.8error bands: χ2
min + 1.04
Improved description? JLab data described
? higher mass polesnot at physical valuesMMD 96, HMD 96, HM 04
GD(Q2) =„1 + Q2
0.71 GeV2
«−2
The Pion Cloud of the Nucleon: Facts and popular Fantasies – Ulf-G. Meißner – MIT, LNS, Mar. 9, 2007 · ◦ C < ∧ O > B •
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SPACE-LIKE FORM FACTORS: NEW CLAS DATACLAS collaboration, to be published
0 0.5 1 1.50
0.02
0.04
0.06
0.08
0.1
0.12
GEn
0.01 0.1 1 100.5
0.6
0.7
0.8
0.9
1
1.1
GMn /(
µ nGD
)
0.001 0.01 0.1 1Q2 [GeV2]
0.4
0.6
0.8
1
GEp /G
D
0.1 1 10Q2 [GeV2]
0.6
0.7
0.8
0.9
1
1.1
1.2
GMp /(
µ pGD
)
0 0.5
1
0 0.1 0.2
1
0 0.2 0.4
1
→ apparent discrepancy to be resolved
The Pion Cloud of the Nucleon: Facts and popular Fantasies – Ulf-G. Meißner – MIT, LNS, Mar. 9, 2007 · ◦ C < ∧ O > B •
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TIME-LIKE FORM FACTORS
• fitting also time-like data more complicated
• experimental extraction ambiguous
− E/M separation
− NN final-state interactions?
similar to J/ψ → ppγ from BESSibirtsev et al., Phys. Rev. D 71 (2005) 054010
similar to B+ → ppK+ from BaBarHaidenbauer et al., Phys. Lett. B 643 (2006) 29
− subthreshold resonance ? (or FSI ?)Antonelli et al., Nucl. Phys. B 517 (1998) 3
• many new proton data (radiative return)BES, CLEO, BaBaR
σ(e+e− ↔ pp, e+e− → nn)
The Pion Cloud of the Nucleon: Facts and popular Fantasies – Ulf-G. Meißner – MIT, LNS, Mar. 9, 2007 · ◦ C < ∧ O > B •
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TIME-LIKE FORM FACTORS
54t [GeV2]
0
0.1
0.2
0.3
0.4
0.5
GMp
15105t [GeV2]
0
0.05
0.1
0.15
0.2
0.25
GMp
4.44.243.83.6t [GeV2]
0.2
0.3
0.4
0.5
0.6
0.7
0.8
GMn
• Only proton data participate in the fits
• All data within one sigma – first time consistent fit w/ space-like ffs
⇒ Need more data on time-like GnM
The Pion Cloud of the Nucleon: Facts and popular Fantasies – Ulf-G. Meißner – MIT, LNS, Mar. 9, 2007 · ◦ C < ∧ O > B •
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ON THE PION CLOUD OF THE NUCLEONHammer, M., Drechsel, Phys. Lett. B 586 (2004) 291
0.0 0.5 1.0 1.5 2.0r [fm]
0.0
0.4
0.8
1.2
4πr2 ρ(
r) [1
/fm] GM
V
GEV
• FW find a very long-ranged contribution ofthe pion could, r ' 2 fmFriedrich, Walcher, EPJ A 17 (2003) 607
• longest range component can be extractedfrom the isovector spectral function
→ separation of the ρ-contribution
→ three methods applied to do this
→ theoretical band
ρVi (r) = 1
4π2
∫ 40M2π
4M2πdt Im GV
i (t) e−r√
t
r(i = E,M)
• much smaller pion cloud contribution for r ≥ 1 fm compared to FW
• results independent of the contributions from t > 40M2π
The Pion Cloud of the Nucleon: Facts and popular Fantasies – Ulf-G. Meißner – MIT, LNS, Mar. 9, 2007 · ◦ C < ∧ O > B •
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GnE(Q2) w/ a BUMP-DIP STRUCTURE
• can one generate a bump-dip structure in the dispersive approach?
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Q2 [GeV2]
0
0.05
0.1 GEn(Q2)
BHM best fit BHM light mass polesFW pheno fitBHM 1 sigma
⇒ yes, but need low-mass poles: MS = 358 MeV & MV = 558 MeV
what shall these be? – not consistent w/ spec ftcs!
The Pion Cloud of the Nucleon: Facts and popular Fantasies – Ulf-G. Meißner – MIT, LNS, Mar. 9, 2007 · ◦ C < ∧ O > B •
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SUMMARY & OUTLOOK
• New dispersive analysis of the nucleon em form factors
• Improved spectral functions ⇒ many results
− better fits w/ inclusion of time-like form factors
− theoretical/systematic uncertainty → bands
• Still to be done
− including pQCD corrections at large-t beyond SCR
− two-photon effects? → fit to X sections
− consequences for the strangeness vector form factors
− and much more . . .
The Pion Cloud of the Nucleon: Facts and popular Fantasies – Ulf-G. Meißner – MIT, LNS, Mar. 9, 2007 · ◦ C < ∧ O > B •